Title

On the embedded primary components of ideals (iv)

Abstract

The results in this paper expand the fundamental decomposition theory of ideals pioneered by Emmy Noether. Specifically, let I be an ideal in a local ring (R, M) that has M as an embedded prime divisor, and for a prime divisor P of I let be the set of irreducible components q of I that are P-primary (so there exists a decomposition of I as an irredundant finite intersection of irreducible ideals that has q as a factor). Then the main results show is maximal in the set of Al-primary components of is an irredundant irreducible decomposition of I such that is Af-primary if and only if i = 1,., k < n, then is an irredundant irreducible decomposition of a MEC of I, and, conversely, if Q is a MEC of I and if is an irredundant irreducible decomposition of such that q1,., qkare the A/-primary ideals in then m = k and is an irredundant irreducible decomposition.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1090/S0002-9947-1995-1249882-7

Publication Date

1-1-1995

Journal Title

Transactions of the American Mathematical Society

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